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Abstract

Knowledge of how to change initial conditions to obtain a specified change in model output is fundamental to data assimilation, Forecast Sensitivity to Observation Impact (FSOI) and singular vectors. Accurate adjoints or transposes of the Tangent Linear Models (TLMs) of non-linear models provide this information. Roughly speaking, traditional TLMs are based on computer codes generated by replacing each line of the parent non-linear models by its TLM. Similarly, traditional adjoints are obtained by taking the adjoint of each line of the TLM code. An appeal of ensemble based TLM and adjoints is that the computer codes upon which they are based are far simpler than those associated with traditional TLMs. Furthermore, provided the computational stencil of the non-linear model remains unchanged, ensemble based TLMs would automatically account for underlying model changes with little or no change to the ensemble based TLM/Adjoint code. Unlike the previously proposed Local Ensemble Tangent Linear Model (LETLM), the accuracy of the Implicit Ensemble TLM (IETLM) introduced here is not compromised by the presence of implicit time-stepping. We also describe and demonstrate adjustments of the IETLM that enable it to maintain its competitive performance when the ensemble perturbations are non-linear.